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# When the lengths of two opposite sides of a square garden

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Intern
Joined: 27 Feb 2013
Posts: 6
Schools: Tepper '17 (II)
When the lengths of two opposite sides of a square garden  [#permalink]

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27 Jun 2014, 13:16
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82% (01:46) correct 18% (02:21) wrong based on 294 sessions

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When the lengths of two opposite sides of a square garden were increased by x meters each and the lengths of the other two sides were decreased by x meters each, the area of the new garden was 64 square meters. What was the area of the original square garden?

(1) The area of the new garden was 80 percent of the area of the original square garden
(2) x = 4
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Joined: 02 Sep 2009
Posts: 54544
Re: When the lengths of two opposite sides of a square garden  [#permalink]

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27 Jun 2014, 13:56
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When the lengths of two opposite sides of a square garden were increased by x meters each and the lengths of the other two sides were decreased by x meters each, the area of the new garden was 64 square meters. What was the area of the original square garden?

Let the side of the original square be a. We are given that the area of the new garden was (a - x)(a + x) = a^2 - x^2 = 64.

We want to find the area of the original square, so the value of a^2.

(1) The area of the new garden was 80 percent of the area of the original square garden --> 64 = 0.8a^2 --> a^2 = 80. Sufficient.

(2) x = 4 --> a^2 - 4^2 = 64 --> a^2 = 80. Sufficient.

Hope it's clear.
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Joined: 06 Jan 2014
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Re: When the lengths of two opposite sides of a square garden  [#permalink]

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05 Jul 2014, 23:03
Bunuel - How do we know that the reduced figure is a rectangle. It might even be a parallelogram where the opposite sides of the square are increased in opposite direction and the other opposite sides are reduced in the opposite direction.

Hope I am able to explain the situation
Senior Manager
Joined: 13 Jun 2013
Posts: 274
Re: When the lengths of two opposite sides of a square garden  [#permalink]

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06 Jul 2014, 02:31
rajmegaurav wrote:
Bunuel - How do we know that the reduced figure is a rectangle. It might even be a parallelogram where the opposite sides of the square are increased in opposite direction and the other opposite sides are reduced in the opposite direction.

Hope I am able to explain the situation

hi, because each internal angle of the square is 90, therefore the new figure will also have the same internal angle of 90 degrees each, that is why the new figure is rectangle and not a parallelogram.
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Joined: 29 Jun 2017
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WE: Engineering (Transportation)
Re: When the lengths of two opposite sides of a square garden  [#permalink]

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10 Sep 2017, 23:02
A initial area and y be original side
AreaA y^2
(y+x)(y-x)=64
1) New area is 0.8 of A
64=0.8A
Sufficient

2) x=4

(y+x)(y-x)=64
Then y can be calculated

Therefore sufficient.

Sent from my iPhone using GMAT Club Forum
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Re: When the lengths of two opposite sides of a square garden   [#permalink] 10 Sep 2017, 23:02
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# When the lengths of two opposite sides of a square garden

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